A curve \(y = f\left( x \right)\) passes through the point P (1, 1) . The normal to the curve at P is \(a(y - 1) + (x - 1) = 0\) . If the slope of the tangent at any point on the curve is proportional to the ordinate of that point, determine the equation of the curve. Hence obtain the area bounded by the y-axis, the curve and the normal to the curve at P.

Solution: The slope of the given normal is obvious from the expression: